If you don't have the time to put in to claim the rewards, then that's just the way it is. It is odd that this quest in particuler is set up in four parts that require you to be progressively higher level to complete (the only event I've seen/heard about that does this), but at the same time that's the way it was designed.

Perhaps SE didn't really feel like the "end boss" was something a brand new adventurer (lvl 13) could handle in the lore. Maybe they felt like that would be cheapening Lightning's strength as a character. It was the design decision they made unfortunately and you just have to deal. In all honesty, what have you lost? A chestpiece that you will likely never, ever wear outside of 5 seconds after obtaining it. Even with the vanity system, do you really want your character to just wear an obviously out of place garment of a character from another game?

I think I would have been more upset by the fact that I would have never gotten to see the final cutscene with Lightning, as that (to me) was a lot cooler than the gear rewards. However, you see to be solely focused on the fact that you are missing out on a vanity chestpiece.